Oh, God, no.
Yes, I want the North Korean government to get its well-deserved comeuppance as much as the next guy, but take a look at Seoul on Google Earth. Now drag northwards until you come to the North Korean border. Not very far, is it? Forget fancy missiles, it's within artillery range. It won't matter that they get "(at most) a couple of miles into South Korean territory." By the time they've done so, one of Asia's financial and industrial capitals will lie in ruins. The fact that the already mostly empty shell of Pyongyang will be razed to the ground shortly thereafter is cold comfort.